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Michael Galarnyk
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Added the start of the machine learning from scratch folder (linear regression for now)
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‎Machine_Learning_from_Scratch/.ipynb_checkpoints/LinearRegression-checkpoint.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h1 align=\"center\"> Linear Regression </h1>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np \n",
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"import matplotlib.pyplot as plt\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"from matplotlib import cm\n",
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"# import warmUpExercise as wue\n",
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"#import computeCost as cc\n",
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"#import gradientDescent as gd"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"data = np.loadtxt('ex1data1.txt', delimiter=\",\")\n",
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"X = data[:,0]\n",
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"y = data[:,1]\n",
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"m = len(y) # number of training examples"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(97L,)"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"X.shape"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(97L, 2L)"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.column_stack((np.ones((m,1)), X)).shape"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Add a column of ones to x (theta<sub>0</sub>)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"X_padded = np.column_stack((np.ones((m,1)), X)) \n",
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"\n",
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"theta = np.zeros((2, 1)) # initialize fitting parameters"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(97L,)"
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]
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},
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"execution_count": 26,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.transpose(y).shape"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(97L, 1L)"
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]
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},
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"execution_count": 36,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# (97L, 1L)\n",
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"np.power(( X_padded.dot(theta) - np.transpose([y]) ), 2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"?np.sum()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def computeCost(X, y, theta):\n",
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"\n",
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" #COMPUTECOST Compute cost for linear regression\n",
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" # J = COMPUTECOST(X, y, theta) computes the cost of using theta as the\n",
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" # parameter for linear regression to fit the data points in X and y\n",
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"\n",
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" # Initialize some useful values\n",
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"\n",
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" m = len(y) # number of training examples\n",
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"\n",
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" # You need to return the following variables correctly \n",
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" J = 0\n",
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"\n",
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" # note that \n",
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"\n",
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" # theta is an (n+1)-dimensional vector \n",
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"\n",
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" # X is an m x (n+1)-dimensional matrix\n",
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"\n",
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" # y is an m-dimensional vector\n",
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"\n",
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" s = np.power(( X.dot(theta) - np.transpose([y]) ), 2)\n",
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"\n",
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" J = (1.0/(2*m)) * s.sum( axis = 0 )\n",
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"\n",
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" return J"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def gradientDescent(X, y, theta, alpha, num_iters):\n",
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"\n",
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" # GRADIENTDESCENT Performs gradient descent to learn theta\n",
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"\n",
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" # theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by \n",
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"\n",
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" # taking num_iters gradient steps with learning rate alpha\n",
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"\n",
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"\n",
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"\n",
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" # Initialize some useful values\n",
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"\n",
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" m = len(y) # number of training examples\n",
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"\n",
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" J_history = np.zeros((num_iters, 1))\n",
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"\n",
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"\n",
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"\n",
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" for i in xrange(num_iters):\n",
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"\n",
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"\n",
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"\n",
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" # ====================== YOUR CODE HERE ======================\n",
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"\n",
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" # Instructions: Perform a single gradient step on the parameter vector\n",
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"\n",
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" # theta. \n",
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"\n",
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" #\n",
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"\n",
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" # Hint: While debugging, it can be useful to print out the values\n",
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"\n",
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" # of the cost function (computeCost) and gradient here.\n",
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"\n",
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" #\n",
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"\n",
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" theta = theta - alpha*(1.0/m) * np.transpose(X).dot(X.dot(theta) - np.transpose([y]))\n",
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"\n",
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" # Save the cost J in every iteration \n",
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"\n",
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" import computeCost as cc\n",
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"\n",
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" J_history[i] = cc.computeCost(X, y, theta)\n",
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"\n",
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" return theta, J_history"
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]
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}
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],
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"metadata": {
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"anaconda-cloud": {},
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"kernelspec": {
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"display_name": "Python [conda root]",
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"language": "python",
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"name": "conda-root-py"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.12"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}

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